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arXiv · 1303.1364

On the tensor degree of finite groups

Peyman Niroomand·Francesco G. Russo
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Abstract

We study the number of elements $x$ and $y$ of a finite group $G$ such that $x \otimes y= 1_{_{G \otimes G}}$ in the nonabelian tensor square $G \otimes G$ of $G$. This number, divided by $|G|^2$, is called the tensor degree of $G$ and has connection with the exterior degree, introduced few years ago in [P. Niroomand and R. Rezaei, On the exterior degree of finite groups, Comm. Algebra 39 (2011), 335--343]. The analysis of upper and lower bounds of the tensor degree allows us to find interesting structural restrictions for the whole group.

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Peyman Niroomand, Francesco G. Russo. 2013-03-06. On the tensor degree of finite groups. https://arxiv.org/abs/1303.1364

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